Stable manifoldIn mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor. In the case of hyperbolic dynamics, the corresponding notion is that of the hyperbolic set. The gravitational tidal forces acting on the rings of Saturn provide an easy-to-visualize physical example. The tidal forces flatten the ring into the equatorial plane, even as they stretch it out in the radial direction.
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
Lyapunov stabilityVarious types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).
BIBO stabilityIn signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded. A signal is bounded if there is a finite value such that the signal magnitude never exceeds , that is For discrete-time signals: For continuous-time signals: For a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response, , be absolutely integrable, i.
RapeRape is a type of sexual assault involving sexual intercourse or other forms of sexual penetration carried out against a person without their consent. The act may be carried out by physical force, coercion, abuse of authority, or against a person who is incapable of giving valid consent, such as one who is unconscious, incapacitated, has an intellectual disability, or is below the legal age of consent. The term rape is sometimes used interchangeably with the term sexual assault.
Food processingFood processing is the transformation of agricultural products into food, or of one form of food into other forms. Food processing includes many forms of processing foods, from grinding grain to make raw flour to home cooking to complex industrial methods used to make convenience foods. Some food processing methods play important roles in reducing food waste and improving food preservation, thus reducing the total environmental impact of agriculture and improving food security.
Food industryThe food industry is a complex, global network of diverse businesses that supplies most of the food consumed by the world's population. The food industry today has become highly diversified, with manufacturing ranging from small, traditional, family-run activities that are highly labour-intensive, to large, capital-intensive and highly mechanized industrial processes. Many food industries depend almost entirely on local agriculture, animal farms, produce, and/or fishing.
Food safetyFood safety (or food hygiene) is used as a scientific method/discipline describing handling, preparation, and storage of food in ways that prevent foodborne illness. The occurrence of two or more cases of a similar illness resulting from the ingestion of a common food is known as a food-borne disease outbreak. This includes a number of routines that should be followed to avoid potential health hazards. In this way, food safety often overlaps with food defense to prevent harm to consumers.
Marital rapeMarital rape or spousal rape is the act of sexual intercourse with one's spouse without the spouse's consent. The lack of consent is the essential element and need not involve physical violence. Marital rape is considered a form of domestic violence and sexual abuse. Although, historically, sexual intercourse within marriage was regarded as a right of spouses, engaging in the act without the spouse's consent is now widely classified as rape by many societies around the world, and increasingly criminalized.
Food engineeringFood engineering is a scientific, academic, and professional field that interprets and applies principles of engineering, science, and mathematics to food manufacturing and operations, including the processing, production, handling, storage, conservation, control, packaging and distribution of food products. Given its reliance on food science and broader engineering disciplines such as electrical, mechanical, civil, chemical, industrial and agricultural engineering, food engineering is considered a multidisciplinary and narrow field.
FoodFood is any substance consumed by an organism for nutritional support. Food is usually of plant, animal, or fungal origin and contains essential nutrients such as carbohydrates, fats, proteins, vitamins, or minerals. The substance is ingested by an organism and assimilated by the organism's cells to provide energy, maintain life, or stimulate growth. Different species of animals have different feeding behaviours that satisfy the needs of their metabolisms and have evolved to fill a specific ecological niche within specific geographical contexts.
Food coloringFood coloring, or color additive, is any dye, pigment, or substance that imparts color when it is added to food or drink. They come in many forms consisting of liquids, powders, gels, and pastes. Food coloring is used in both commercial food production and domestic cooking. Food colorants are also used in a variety of non-food applications, including cosmetics, pharmaceuticals, home craft projects, and medical devices. People associate certain colors with certain flavors, and the color of food can influence the perceived flavor in anything from candy to wine.
Food securityFood security is the availability of food in a country (or geography) and the ability of individuals within that country (geography) to access, afford, and source adequate foodstuffs. According to the United Nations Committee on World Food Security, food security is defined as meaning that all people, at all times, have physical, social, and economic access to sufficient, safe, and nutritious food that meets their food preferences and dietary needs for an active and healthy life.
Food systemThe term food system describes the interconnected systems and processes that influence nutrition, food, health, community development, and agriculture. A food system includes all processes and infrastructure involved in feeding a population: growing, harvesting, processing, packaging, transporting, marketing, consumption, distribution, and disposal of food and food-related items. It also includes the inputs needed and outputs generated at each of these steps.
Herfindahl–Hirschman indexThe Herfindahl index (also known as Herfindahl–Hirschman Index, HHI, or sometimes HHI-score) is a measure of the size of firms in relation to the industry they are in and is an indicator of the amount of competition among them. Named after economists Orris C. Herfindahl and Albert O. Hirschman, it is an economic concept widely applied in competition law, antitrust regulation, and technology management. HHI has continued to be used by antitrust authorities, primarily to evaluate and understand how mergers will affect their associated markets.
X-rayX-ray radiation, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 nanometers to 10 picometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz (3e16Hz to 3e19Hz) and energies in the range 124 keV to 145 eV, respectively. X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays.
